On the discrete mean square of Dirichlet L-functions at 1

Abstract

There have been many results obtained so far for the mean square of the (absolute) value of the Dirichlet L-function L(s,χ) in the critical strip 0<σ<1, especially on the critical line Open image in new window , but relatively few results were known for discrete mean value of |L(1,χ)|2 till W. Zhang had published papers improving the error term step by step, which have recently been superseded by M. Katsurada and K.Matsumoto in which they succeeded in deriving an ‘‘asymptotic formula’’ for ∑χ≠χ0|L(1, χ)|2. The object of our paper is to point out a structural property contained in the formation of the mean square, to find out the niryana–the true body of the above sum.